Reset times-dependent stability of reset control systems

Reset control systems are a special type of hybrid systems in which the time evolution depends both on continuous dynamics between resets and the discrete dynamics corresponding to the reset instants. In this work, stability of reset control systems is approached by using an equivalent (time-varying) discrete time system, introducing necessary and sufficient stability conditions that explicitly depends on the reset times. These conditions have been simplified for the case in which the linear base control system is stable, resulting in a sufficient condition that only depends on a lower bound of the reset intervals.